System for and method of determining angular position of a vehicle

ABSTRACT

A system for and method of determining angular position (e.g. pitch) of a vehicle. In accordance with an embodiment, a first angular rate of rotation of the vehicle about a first axis of rotation is detected using a first angular rate sensor mounted to the vehicle. A second angular rate of rotation of the vehicle about a second axis of rotation is detected using a second angular rate sensor mounted to the vehicle. The second axis of rotation is substantially orthogonal to the first axis of rotation. The angular position of the vehicle is determined based on a ratio of the first angular rate of rotation of the vehicle and the second angular rate of rotation of the vehicle.

BACKGROUND OF THE INVENTION

The present invention relates to the field of vehicle position sensingand, more particularly, the present invention relates to sensing anangular position of a vehicle, such as its roll, pitch or yaw.

Owing to their precision and accuracy, Global Navigation SatelliteSystems (GNSS) have become the de facto standard for vehicle navigationsolutions. However, in automotive applications, the prerequisite ofhaving line-of-sight view of the sky is not always met. For instance,around high-rise buildings, dense foliage, in tunnels and under stackedroads and rooftops, GNSS reception is severely compromised.

Dead reckoning refers to the process of augmenting GNSS position fixeswith additional sensor information to deduce the vehicle's positionduring GNSS outage. One type of sensor that is often used in deadreckoning is the vehicle wheel sensor, which can provide information onthe distance travelled when GNSS signals are unavailable. Typicallythese count the number of wheel revolutions via an axle encoder placedon the wheel axle.

However, dead reckoning position updates based purely on wheel rotationhave their limitations because vehicles can move in three dimensions.Take for instance a vehicle travelling a distance L up an incline of 30degrees, as illustrated in FIG. 1. The wheel encoder would deduce adistance L from the start of the ramp although the actual distancetravelled in the horizontal direction is only 0.87 L. Hence, the deadreckoning error is a 13% overestimate in the horizontal direction and noindication is provided of the distance travelled in the verticaldirection. Using differential wheel rotation, e.g., a separate encoderon the left rear wheel and another encoder on the right rear wheel, canallow dead reckoning in two dimensions, however, this still does notprovide any information about movement in the third dimension.

For this reason, many modern dead reckoning systems employ a host ofadditional sensors, such as accelerometers and gyroscopes, to detectvehicle movements. Having knowledge of the angular position of thevehicle can greatly improve the position estimate of the vehicle whenGNSS signals are unavailable. In the foregoing example, having knowledgeof the vehicle's pitch would allow a more accurate determination of thevehicle's position in three dimensions. As discussed in the following,there are various known techniques to determine the pitch of thevehicle.

Gyroscope Only Approach

In principal, a gyroscope perfectly aligned with the traverse axis(y-axis) of the body of a vehicle can be used to determine the vehicle'spitch. Although simple, there are several reasons why pitchdetermination based only on such a gyroscope measurement is not veryaccurate.

One issue associated with using gyroscopes is caused by the nature ofthe sensor itself. Gyroscopes only provide an angular rate and not anabsolute measure of the angle. To obtain the latter, the output from thegyroscope needs to be integrated. However without knowledge of theinitial conditions, i.e. the initial pitch of the body in which thegyroscope is mounted, the calculated output will be in error unless theinitial pitch of the body is zero at t=0.

Secondly, since gyroscopes only indicate a rate of change of angulardisplacement, the measurements in some circumstances are of extremelyshort duration. Imagine for instance a vehicle traversing from levelground onto a ramp with a constant slope. The output of a y-axisgyroscope would register the change in pitch angle at the instant thevehicle enters the ramp. However, this measurement would only exist fora very short duration before returning to zero as the vehicle climbs theramp. The very short duration of the measurement makes it challenging toobtain reliable results, especially if the pitch is used to deduce thevehicle's altitude.

Multi-Sensor Approach

More commonly, gyroscopes are used together with accelerometers for moreaccurate determination of angular position. In determining the pitch ofa vehicle, accelerometers often provide more reliable results. In thecase of a vehicle traversing a ramp as discussed earlier, anaccelerometer would continuously provide a measurement while travellingup the constant incline even though the pitch hasn't changed. This isbecause the accelerometer provides a measurement of the accelerationsthe vehicle is experiencing.

One way of taking advantage of both types of sensors to determine anaccurate pitch angle involves calculating the difference of the twoangles determined by each type of sensor and feeding back this ‘error’difference to correct the pitch angle measured by the gyroscope sensor.The output of the gyroscope is integrated as before, except this time itis correlated with information indirectly gathered from theaccelerometer sensor.

Accelerometer Only Approach

The pitch of a stationary or non-accelerating vehicle can also bedetermined using a single accelerometer. For example, an accelerometersensing longitudinal (x-axis) acceleration of a vehicle parked or movingwith constant velocity along an incline can be used to directly deducethe incline angle or pitch of the vehicle (according to A_(X)=1g×sin(θ), where A_(X) denotes the accelerometer output and θ is thepitch of the vehicle). However, such a determination is only accuratewhen the sensor is oriented correctly in the vehicle. Otherwise, anyrotation about the other axes affects the magnitude of the accelerationsensed along the vehicle's x-axis and thus introduces an error into thepitch calculation. Furthermore, if the vehicle is moving with non-zeroacceleration, a means is additionally required to determine theacceleration of the vehicle due to its own forward motion. This extracomponent of acceleration then needs to be accounted for and subtractedfrom the acceleration sensed by the accelerometer.

What is needed are improved techniques for determining the angularposition of a vehicle.

SUMMARY OF THE INVENTION

The present invention provides a system for and method of determiningangular position (e.g. pitch) of a vehicle. In accordance with anembodiment, a first angular rate of rotation of the vehicle about afirst axis of rotation is detected using a first angular rate sensormounted to the vehicle. A second angular rate of rotation of the vehicleabout a second axis of rotation is detected using a second angular ratesensor mounted to the vehicle. The second axis of rotation issubstantially orthogonal to the first axis of rotation. The angularposition of the vehicle is determined based on a ratio of the firstangular rate of rotation of the vehicle and the second angular rate ofrotation of the vehicle.

In accordance with a further embodiment of the present invention, afirst angular rate of rotation of the vehicle about a first axis ofrotation is detected using a first angular rate sensor mounted to thevehicle. A second angular rate of rotation of the vehicle about a secondaxis of rotation is detected using a second angular rate sensor mountedto the vehicle. The second axis of rotation is substantially orthogonalto the first axis of rotation. The angular position of the vehicle isestimated using the first angular rate of rotation of the vehicle andthe second angular rate of rotation of the vehicle. A change in locationof the vehicle is estimated using the estimated angular position of thevehicle.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is described with respect to particular exemplaryembodiments thereof and reference is accordingly made to the drawings inwhich:

FIG. 1 illustrates a vehicle deploying a wheel sensor for dead reckoningin accordance with conventional methods;

FIG. 2 illustrates a block schematic diagram of a system for determiningan angular position of a vehicle in accordance with an embodiment of thepresent invention;

FIG. 3 illustrates a vehicle for which pitch is determined in accordancewith an embodiment of the present invention;

FIG. 4 illustrates a spiral car ramp upon which a traveling vehicle'sangular position can be determined in accordance with an embodiment ofthe present invention;

FIG. 5 illustrates a vehicle for which roll is determined in accordancewith an embodiment of the present invention;

FIG. 6 illustrates a misalignment between a vehicle body frame andsensor frame that can be accounted for in accordance with an embodimentof the present invention;

FIG. 7 illustrates a heading of a vehicle being determined by a z-axisangular rate sensor when travelling on flat ground in accordance with anembodiment of the present invention;

FIGS. 8a-b illustrate vehicle movement in a car park obtained withoutactivation of the present invention;

FIGS. 9a-b illustrate vehicle movement in a car park obtained inaccordance with an embodiment of the present invention; and

FIGS. 10a-b illustrate vehicle movement in a car park obtained withsensor misalignment correction in accordance with a further embodimentof the present invention.

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT OF THE INVENTION

The present invention provides a system for and method of determiningangular position of a vehicle. As an illustrative example, the presentinvention is described herein in connection with determining angularposition of an automobile. However, the vehicle can be any objectcapable of movement from one place to another and of experiencing changein angular position and that is of sufficient size that angular ratesensors described herein can be mounted thereto. Examples of suchvehicles include, but are not limited to, land vehicles (includingautomobiles, trucks and construction equipment), aircraft (includingairplanes and helicopters) and watercraft (including submersibles). Thedetermined angular position can be any one or more of roll, pitch oryaw. For reference, the vehicle is considered to have a longitudinalaxis, a transverse axis and a vertical axis. The origin of all threeaxes may be defined to be the center of the vehicle (e.g., its center ofgravity). However, other definitions are possible. For example, themiddle of the rear axle of an automobile may be defined to be the originof the axes.

The longitudinal axis (also referred to as the x-axis or roll axis)extends from the origin and exits the front of the vehicle. Thus, thevehicle's straight-line forward motion is generally aligned with thelongitudinal axis. The angular position of the vehicle about thelongitudinal axis is referred to as “roll.” In the case of anautomobile, roll refers to lateral tilt experienced by the vehicle forinstance when it negotiates a curve and or banked roadway. Thetransverse axis (also referred to as the y-axis or pitch axis) extendsfrom the origin, exits the right side of the vehicle (starboard side ofa boat) and is orthogonal to the longitudinal axis. The angular positionof the vehicle about the y-axis is referred to as “pitch” and indicatesthe extent to which the vehicle has a nose-up attitude (positive pitch)or nose-down attitude (negative pitch). The vertical axis (also referredto as the z-axis or yaw axis) extends from the origin, exits the bottomof the vehicle and is orthogonal to both the longitudinal axis and thetransverse axis. The angular position of the vehicle about the z-axis isreferred to as “yaw” or heading.

The present invention involves obtaining angular rate sensormeasurements about two of the three orthogonal axes of the vehicle andusing those measurements to estimate the angular position of the vehicleabout a third axis. The angular position is estimated without requiringthe use of accelerometers. For example, the vehicle pitch (angularposition about the y-axis) can be determined if measurements from anx-axis (roll) sensor and a z-axis (yaw) sensor are available and if asignificant yaw rate is observed. This approach enables a change inaltitude determination in dead reckoning mode and provides thepossibility to improve the accuracy of the heading as well. Noaccelerometers are required. The performance can be improved further ifthe estimated pitch is used to align the sensor axes to the axes of thevehicle frame to account for any misalignment.

As another example, the vehicle roll (angular position about the x-axis)can be determined if measurements from a y-axis (pitch) sensor and az-axis (yaw) sensor are available and if a significant yaw rate isobserved.

FIG. 2 illustrates a block schematic diagram of a system for determiningangular position of a vehicle 100 in accordance with an embodiment ofthe present invention. The vehicle 100 has mounted thereon a firstangular rate sensor 102 and a second angular rate sensor 104. The firstangular rate sensor 102 and the second angular rate sensor 104 arepreferably mounted to the vehicle such that their measurement axes aresubstantially parallel to the vehicle body axes and substantiallyorthogonal to each other. A processor 106 is configured to receivemeasurement data signals from the first angular rate sensor 102 and thesecond angular rate sensor 104. The processor 106 is further configuredto compute an estimate of the angular position of the vehicle based onthe sensor data signals. The angular rate sensors 102 and 104 caninclude gyroscopes or gyroscope equivalents, including but not limitedto, MEMS gyroscope, fiber optic gyroscope, vibrating structuregyroscope, or other type of angular rate sensor. Moreover, the first andsecond angular rate sensors 102 and 104 can be housed together as aunit, for example, they can be implemented as a dual-axial gyroscope.

As explained herein, the processor 106 can additionally determine achange in location of the vehicle using the estimated angular positionof the vehicle. For example, the processor 106 can use the estimatedangular position, along with other information such as vehicle speedinformation obtained from, for example, wheel rotation sensors or aspeedometer, to estimate a change in location of the vehicle. In deadreckoning mode, the processor 106 can determine estimates of currentlocations of the vehicle based on an initial location and an initialangular position of the vehicle obtained from GNSS signals and theestimated angular position of the vehicle obtained based on informationfrom the sensors 102 and 104. Thus, as shown in FIG. 2, the vehicle canoptionally include a GNSS receiver 108 in communication with theprocessor 106 in order to obtain GNSS information that can be used bythe processor 106 in conjunction with other information.

A display 110 can optionally be provided within the vehicle 100 todisplay estimated vehicle angular positions and location information toan operator of the vehicle 100. Such information can alternatively oradditionally be communicated to a remote location (e.g., a remote servercommunicatively coupled to the vehicle 100 via cellular or wirelesssignaling) for collecting, saving and potentially performing additionalprocessing on the information.

FIG. 3 shows a vehicle 100 for which angular position, namely pitch, canbe determined in accordance with the present invention. In thisexemplary embodiment, the first angular rate sensor 102 is aligned withthe roll axis (x-axis) of the vehicle 100 while the second angular ratesensor 104 is aligned with the yaw axis (z-axis) of the vehicle 100. Theangular rate sensors 102 and 104 measure the angular rates of rotationabout their respective axis. As shown in FIG. 3, the angular ratesensors 102 and 104 can be incorporated into a dual-axial sensor 112.Note that two coordinate systems are shown in FIG. 3, namely, aninertial reference frame (X_(i), Z_(i)) and a vehicle body frame (X_(b),Z_(b)). These two frames are described further under the mathematicalderivation given herein.

Pitch Determination Using Two Angular Rate Sensors

As explained herein, using solely a traverse or y-axis gyroscope todetermine the pitch of a vehicle is usually inaccurate and thereforeavoided. The present invention is based on the realization that undercertain circumstances two orthogonally positioned gyroscopes can be usedto accurately determine the pitch of a vehicle. Specifically, when avehicle experiences significant rotation (or yaw) around its verticalaxis (z-axis), an accurate pitch determination can be provided by alongitudinally (x-axis) positioned gyroscope and a vertically (z-axis)positioned gyroscope in the vehicle body according to:

$\begin{matrix}{\theta = {\tan^{- 1}\left( \frac{- G_{X}}{G_{Z}} \right)}} & (1)\end{matrix}$

where θ represents the pitch of the body (vehicle) in which thegyroscopes are mounted and G_(X) and G_(Z) are the measurements from thelongitudinal (or x-axis gyroscope) and the vertical (or z-axisgyroscope), respectively.

The only assumptions are that the vehicle experiences a significantrotation around the vertical axis (z-axis) and the rate of change ofroll around the traverse axis (x-axis) of the vehicle (and the rollangle itself) is negligible. The first assumption will be valid wheneverthe vehicle is turning while travelling, for example ascending ordescending a spiral ramp in a car park. FIG. 4 illustrates an exemplaryspiral car ramp upon which a traveling vehicle's angular position can bedetermined.

The second assumption is generally true for most road surfaces overwhich vehicles travel. This is because roads are purposely built tominimize vehicle roll and thus roll angles are usually negligible.

The invention has three key advantages. The first is that it allowsaccurate pitch determination in vehicles without deployment ofaccelerometers. This is particularly useful in applications where onlygyroscopes are available. Secondly, compared to the single accelerometerapproach described earlier, acceleration information is not required inthe pitch determination even if the vehicle is moving with non-uniformmotion. Thirdly, having accurate pitch information allows for animproved heading determination of the vehicle when ascending ordescending as explained herein.

Mathematical Derivation

In order to show the validity of equation (1) it is useful to define twocoordinate frames, namely an inertial reference frame and a vehicle bodyframe. The inertial reference frame is a stationary set of axes in afixed position with respect to the earth. For the purposes of thederivation and discussion, a common aerospace inertial reference frameis adopted where the x-axis points north, the y-axis points east and thez-axis points below (known as the North-East-Down or NED referenceframe). Note that because the z-axis is defined as downwards, anyaltitude above ground is negative.

In most applications, the axes of sensors such as gyroscopes are made tocoincide with the axes of the moving platform in which the sensors aremounted, e.g. a vehicle. In the following derivation the vehicle bodyframe x-axis is defined as pointing out of the vehicle's windscreen, they-axis points laterally through the vehicle doors and the body framez-axis points downwards beneath the vehicle. The sensor frame coincideswith the body frame though, as discussed herein, there can bemisalignment between the vehicle body frame and sensor frame.

The sensors (e.g. gyroscopes) mounted on the vehicle report rotationrates with respect to the vehicle body frame. Thus in order to determinethe Euler Angle rates of the vehicle, i.e. the pitch rate, {dot over(θ)}, the roll rate, {dot over (φ)} and the yaw rate, {dot over (ψ)}, itis first necessary to convert them to measurements made by the sensorsin the appropriate coordinate frame, i.e. to the inertial referenceframe. This can be done by performing a series of transformations. Thetransformation matrix for converting angular rate measurements made bysensors on the vehicle's body to Euler angular rates in the inertialreference frame is given by

$\begin{matrix}{{D\left( {\varphi,\theta,\psi} \right)} = \begin{bmatrix}1 & {\sin \; \varphi \; \tan \; \theta} & {\cos \; {\varphi tan}\; \theta} \\0 & {\cos \; \varphi} & {{- \sin}\; \varphi} \\0 & {\sin \; {\varphi/\cos}\; \theta} & {\cos \; {\varphi/\cos}\; \theta}\end{bmatrix}} & (2)\end{matrix}$

If G_(X) represents the vehicle body frame x-axis sensor reading, Gy thevehicle body frame y-axis sensor reading and G_(Z) the z-axis sensorreading, then it can be shown that the Euler Angle rates are givenaccording to

$\begin{matrix}{\begin{bmatrix}\overset{.}{\varphi} \\\overset{.}{\theta} \\\overset{.}{\psi}\end{bmatrix} = \begin{bmatrix}{G_{X} + {G_{Y}\sin \; \varphi \; \tan \; \theta} + {G_{Z}\cos \; \varphi \; \tan \; \theta}} \\{{G_{Y}\cos \; \varphi} - {G_{Z}\sin \; \varphi}} \\{{G_{Y}\sin \; {\varphi/\cos}\; \theta} + {G_{Z}\cos \; {\varphi/\cos}\; \theta}}\end{bmatrix}} & (3)\end{matrix}$

Considering only the rate of roll component, i.e. the first row of thematrix in equation (3), it follows that

{dot over (φ)}=G _(X) +G _(Y) sin φ tan θ+G _(Z) cos φ tan θ  (4)

Under the assumption the roll and rate of change of roll are negligible,i.e.

φ≈0 and {dot over (φ)}≈0

Then equation [4] becomes

0=G _(X) +G _(Z) tan θ  (5)

and rearranging equation (5) for the pitch θ finally yields

θ=tan⁻¹(−G _(X) /G _(Z))

as required by equation (1).

Roll Determination Using Two Angular Rate Sensors

The invention can be used to accurately measure roll of a vehicle.Specifically, angular position about the x-axis of the vehicle (roll)can be determined using a lateral (y-axis) gyroscope and a vertical(z-axis gyroscope).

FIG. 5 shows a vehicle 100 for which roll can be determined inaccordance with the present invention. In this exemplary embodiment, thefirst angular rate sensor 102 is aligned with the pitch axis (y-axis) ofthe vehicle 100 while the second angular rate sensor 104 is aligned withthe yaw axis (z-axis) of the vehicle 100. The back of the vehicle 100 isshown in FIG. 5, as the vehicle is oriented as though it is travellinginto the page. The angular rate sensors 102 and 104 measure the angularrates of rotation about their respective axis. Similarly to FIG. 3, twocoordinate systems are shown in FIG. 5, namely, an inertial referenceframe (X_(i), Z_(i)) and a vehicle body frame (X_(b), Z_(b)).Furthermore, the angular rate sensors 102 and 104 may be incorporatedinto a dual-axial sensor 112.

As with the pitch determination, a significant yaw rate should bepresent. In addition, the rate of change in pitch should be small. Themathematical derivation for roll determination is as follows:

Using the second row of matrix given previously in Equation (3) above:

{dot over (θ)}=G _(Y) cos φ−G _(Z) sin φ  (6)

Assuming constant pitch, i.e. rate of change of pitch to be negligible.Equation (6) becomes:

0=G _(Y) cos φ−G _(Z) sin φ  (7)

Rearranging equation (7) for the roll yields:

$\frac{\sin \; \varphi}{\cos \; \varphi} = \frac{G_{Y}}{G_{Z}}$

Hence the roll of the vehicle is determined by:

φ=tan⁻¹(G _(Y) /G _(Z))

Sensor Misalignment Correction

To this point, any misalignment between the inertial sensor frame andthe vehicle body frame has not been taken into account. For simplicity,it has been assumed that the sensors have been installed such that theyare perfectly aligned with the vehicle. In other words, it has beenassumed that the angular difference between the vehicle body frame andeach gyroscope's axis of rotation is zero, i.e. the axes of the sensorframe are parallel to the axes of the vehicle body frame.

In practice, there will almost always be some misalignment due either toimperfect mounting of the two or more gyroscopes within the sensors'housing or imperfect alignment of the sensor housing within the vehicleitself upon installation. FIG. 6 illustrates a misalignment between avehicle body frame (b) and sensor frame (s) that can be taken intoaccount. This misalignment will affect any angles determined from sensormeasurements. Thus the observed pitch θ determined by equation (1) willconsist of the true pitch θ_(T) of the vehicle and a pitch misalignmenterror Δθ_(err), i.e.

θ=θ_(T)+Δθ_(err)  (8)

Therefore, according to equation (8) in order to obtain an accuratevalue for the pitch of the vehicle, the error contribution Δθ_(e), dueto sensor misalignment should be removed from the pitch determined byequation (1). The sensor misalignment is a single angle which representsthe angular displacement between the vehicle body x-z plane and thesensor x-z plane. In simple terms, the pitch misalignment error Δθ_(e),is subtracted from every pitch angle derived to obtain the true pitchθ_(T) of the vehicle. This requires prior knowledge of the pitchmisalignment error Δθ_(err).

The pitch misalignment error Δθ_(err) can be viewed as the fixed angleof rotation between the sensor frame of the real mounted gyroscopes andthat of ideally mounted gyroscopes (which would be perfectly alignedwith the vehicle body frame). One way to obtain the pitch misalignmenterror Δθ_(err) is to determine the vehicle pitch using a method thatdoes not involve utilization of the onboard inertial sensors and comparethe result with the pitch determined from using equation (1). Forexample, when GNSS signals are available one may deploy traditionalpositioning techniques to independently determine the pitch of thevehicle. This could be done initially at start-up of the system during acontrol or calibration drive before the sensors are configured forofficial use. Alternatively, the misalignment error could becontinuously calibrated whenever GNSS signals are available in order todetect any variation of the sensor misalignment e.g. due to the changeof the vehicle payload. It is important to note that the calibrationdrive need not be performed over level ground.

Rate of Change of Heading Correction

If the vehicle traverses over perfectly level ground, the reading fromthe vertical or yaw (z-axis) gyroscope will provide a direct indicationof the vehicle's rate of change of heading {dot over (ψ)} (also referredto as the turn or yaw rate). The heading or the direction the vehicle istravelling can hence be updated by integrating the vehicle's rate ofchange of heading if the initial heading ψ₀ is known. FIG. 7 shows theheading of the vehicle relative to the inertial reference andvehicle-body frames. Similarly, if the vehicle was to travel up aninfinitely steep slope such as a wall (hypothetical situation), thereading from the roll (x-axis) gyroscope would indicate the vehicle'srate of change of heading or yaw rate. In these two orthogonalsituations the reading on the other gyroscope would be zero, i.e.driving on level ground G_(Y)=0 and driving up a wall G_(Z)=0.

Only in these two circumstances do the gyroscope measurements given anaccurate indication of the vehicle's rate of change of heading. However,in reality the ground over which a vehicle traverses is rarelycompletely flat and never infinitely steep. Consequently, the rate ofchange of heading information obtained from the sensors will usuallyhave components in both the x-axis and z-axis directions.

Knowledge of the vehicle's pitch however can be used to ‘correct’ orresolve the vehicle's rate of change of heading when the vehicle is nottraversing over level ground. Either of the following equations (9) or(10) will provide the vehicle's ‘true’ yaw rate

$\begin{matrix}{\overset{.}{\psi} = \frac{G_{Z}}{\cos \; \theta_{T}}} & (9) \\{\overset{.}{\psi} = \frac{- G_{X}}{\sin \; \theta_{T}}} & (10)\end{matrix}$

Although both equations will provide the true yaw rate, employment ofequation (9) is preferred numerically because it doesn't return adiscontinuity when the vehicle is travelling on level ground. Inaddition, for small pitch angles, the denominator will be typicallylarger and thus less influenced by systematic errors.

The pitch determination and, following, heading correction may beperformed only if a significant rate of change in vehicle yaw isdetected. For instance, a yaw rate threshold, e.g. of five degrees persecond, might be defined such that corrections to the vehicle's headingare only carried out if the yaw rate exceeds this threshold. Thedefinition of the threshold may be made with respect to the quality ofthe gyroscope measurements. A higher threshold might be set if thequality of the gyroscope measurements is low.

Altitude Propagation

Knowledge of the vehicle's true pitch also allows propagation of thevehicle's altitude independently of GNSS. This is particularlyadvantageous in scenarios where the vehicle is climbing/descending andsatellite signals either unavailable or the reception of such signals iscompromised. Examples of situations in which GNSS signals may beunavailable or compromised in connection with automobiles or trucksinclude ramps in multi-level car parks, curved ramps within tunnels,curved roads passing through valleys and canyons, such as mountainroads, roadways within open pit mining sites, urban environments whereGNSS signals are blocked or impeded by structures like high-risebuildings, and other similar conditions.

The altitude just prior to the loss of GNSS signals, e.g., at theentrance to a car park or tunnel, will be available from the lastposition fix determined via GNSS or via a fused solution utilizing GNSSand sensor measurements. Thereafter, while GNSS signals are unavailable,e.g., after the vehicle enters the car park or tunnel, the new altitudecan be calculated from

z(t ₁)=z(t ₀)−vΔT sin θ_(T)  (11)

irrespective of whether GNSS signals are available. Here z(t₁), z(t₀), vand ΔT refer to the altitude of the vehicle at the current epoch,altitude at the previous epoch, velocity of the vehicle and time periodbetween the two epochs, respectively. Note that a positive angle willreturn a negative height because the local inertial reference frameassumes downward travel along the z-axis. The velocity may be determinedfrom the speedometer or a device which measures the number of wheelrevolutions in a given time. The velocity may alternatively come fromthe last known velocity of the vehicle before GNSS reception was lost.Alternatively, the velocity may be determined from an accelerometermeasurement, if one or more accelerometers are available.

Altitude propagation as described herein requires a GNSS receiver orsome other means to measure absolute altitude, e.g. a barometer, and twoangular rate sensors, such as a dual-axis (roll and yaw or XZ)gyroscope, fitted in the vehicle. Note that a tri-axis (roll, pitch andyaw or XYZ) gyroscope may also be employed where the pitch gyroscope issimply not used. In other words, a dual-axis of a tri-axis gyroscope maybe utilized. This later implementation may be preferable due to theubiquity of tri-axis gyroscopes and reduced costs from greaterintegration. If altitude information is desired then the implementationadditionally requires a means to determining the velocity, e.g. inputfrom a wheel sensor or a speedometer.

The altitude propagation and heading correction calculations can beperformed in the receiver's firmware which resides on the hostmicroprocessor inside the GNSS receiver. The pitch can be calculated asdescribed herein.

As previously mentioned, the invention does not require the deploymentof accelerometers. However, should accelerometers be additionallyavailable, the pitch determination using gyroscopes as discussed abovewould provide an independent measurement which could be combined withthe pitch determined from the accelerometers in order to obtain a moreaccurate and reliable pitch measurement.

A series of test drives conducted in a car park using the invention isshown in FIGS. 8a-b, 9a-b and 10a-b . The black lines in each of FIGS.8, 9 and 10 represent a control trajectory (or actual vehicle path),whereas the grey lines represent a computed trajectory of the vehicle.The top portions (FIGS. 8a, 9a and 10a ) show latitude vs. longitude andrepresent a bird's eye view of the control vehicle trajectory (shown inthe black lines) compared to a computed trajectory (shown in the greylines). The bottom portions (FIGS. 8b, 9b and 10b ) show altitude vs.time with the control vehicle altitude profile shown in the black linescompared to the computed altitude profile shown in the grey lines. FIGS.8a-b show movement of the vehicle in the car park without the inventionactivated (gyroscopes are present but are not used to determine thepitch). Furthermore, the graph in FIG. 8b shows that altitude of thevehicle is not deduced, but is instead maintained constant while GNSSsignals are unavailable and until GNSS signals are again available (atthe exit of the park garage). FIGS. 9a-b show the same movement, thistime using the gyroscopes to determine the pitch and the altitude, inaccordance with the invention. Finally, FIGS. 10a-b show the inventionwith the additional feature of the sensor misalignment correction. Notethat the vehicle uses wheel revolution sensors to determine thevehicle's velocity in the plots, which is needed to calculate thevehicle's altitude.

The foregoing detailed description of the present invention is providedfor the purposes of illustration and is not intended to be exhaustive orto limit the invention to the embodiments disclosed. Accordingly, thescope of the present invention is defined by the appended claims.

1. A method of determining an angular position of a vehicle, comprising:detecting a first angular rate of rotation of the vehicle about a firstaxis of rotation using a first angular rate sensor mounted to thevehicle; detecting a second angular rate of rotation of the vehicleabout a second axis of rotation using a second angular rate sensormounted to the vehicle, the second axis of rotation being substantiallyorthogonal to the first axis of rotation; and estimating the angularposition of the vehicle based on a ratio of the first angular rate ofrotation of the vehicle and the second angular rate of rotation of thevehicle.
 2. The method according to claim 1, wherein the angularposition comprises a pitch of the vehicle.
 3. The method according toclaim 1, wherein the angular position comprises roll of the vehicle. 4.The method according to claim 1, wherein said first axis of rotationcoincides with a roll axis of the vehicle and said second axis ofrotation coincides with a yaw axis of the vehicle.
 5. The methodaccording to claim 1, wherein said detecting the first angular rate ofrotation of the vehicle and said detecting the second angular rate ofrotation of the vehicle are performed simultaneously while the vehicleexperiences significant rate of change of rotation about the secondaxis.
 6. (canceled)
 7. The method according to claim 4, wherein thevehicle experiences a rate of change of rotation about the first axisthat is negligible while said detecting the first angular rate ofrotation of the vehicle and said detecting the second angular rate ofrotation of the vehicle are performed and wherein the vehicle travelsupon a curved ramp while said detecting the first angular rate ofrotation of the vehicle and said detecting the second angular rate ofrotation of the vehicle are performed.
 8. The method according to claim1, further comprising: storing a first parameter representative of thefirst angular rate of rotation of the vehicle in a computer-readabledata storage; and storing a second parameter representative of thesecond angular rate of rotation of the vehicle in the computer-readabledata storage.
 9. The method according to claim 8, wherein saidestimating the angular position of the vehicle is performed by aprocessor using the first parameter representative of the first angularrate of rotation of the vehicle and the second parameter representativeof the second angular rate of rotation of the vehicle.
 10. The methodaccording to claim 1, wherein said estimating the angular position ofthe vehicle comprises determining the inverse tangent of a ratio of saidfirst angular rate of rotation and said second angular rate of rotation.11. (canceled)
 12. The method according to claim 2, further comprisingestimating a change in altitude of the vehicle using the estimated pitchof the vehicle.
 13. The method according to claim 2, further comprisingestimating a position of the vehicle in three dimensions using theestimated pitch of the vehicle.
 14. The method according to claim 1,further comprising calibrating an alignment of the first and secondangular rate sensors with the vehicle.
 15. The method according to claim14, wherein said calibrating the alignment is performed periodicallywhen GNSS signals are available.
 16. (canceled)
 17. The method accordingto claim 2, further comprising resolving a rate of change of heading ofthe vehicle using the estimated pitch of the vehicle and wherein saidresolving the rate of change of heading is performed only when a yawrate of the vehicle exceeds a threshold yaw rate value.
 18. An apparatusconfigured to be mountable to a vehicle for determining an angularposition of the vehicle, comprising: a first angular rate sensorconfigured to detect a first angular rate of rotation of the vehicleabout a first axis of rotation; a second angular rate sensor configuredto detect a second angular rate of rotation of the vehicle about asecond axis of rotation, the second axis of rotation being substantiallyorthogonal to the first axis of rotation; and a processor configured toestimate the angular position of the vehicle based on a ratio of thefirst angular rate of rotation of the vehicle and the second angularrate of rotation of the vehicle.
 19. The apparatus according to claim18, wherein the angular position comprises a pitch of the vehicle. 20.The apparatus according to claim 18, wherein the angular positioncomprises a roll of the vehicle.
 21. The apparatus according to claim18, wherein said first axis of rotation coincides with a roll axis ofthe vehicle and said second axis of rotation coincides with a yaw axisof the vehicle.
 22. The apparatus according to claim 18, wherein theapparatus is configured to detect the first angular rate of rotation ofthe vehicle and the second angular rate of rotation of the vehiclesimultaneously while the vehicle experiences significant rate of changeof rotation about the second axis.
 23. (canceled)
 24. The apparatusaccording to claim 18, wherein the apparatus is configured to detect thefirst angular rate of rotation of the vehicle and the second angularrate of rotation of the vehicle simultaneously while the vehicleexperiences a rate of change of rotation about the first axis that isnegligible and wherein the apparatus is configured to detect the firstangular rate of rotation of the vehicle and the second angular rate ofrotation of the vehicle while the vehicle travels upon a curved ramp.25. The apparatus according to claim 18, further comprising acomputer-readable date storage configured to store a first parameterrepresentative of the first angular rate of rotation of the vehicle anda second parameter representative of the second angular rate of rotationof the vehicle.
 26. The apparatus according to claim 25, wherein theprocessor is configured to estimate the angular position of the vehicleusing the first parameter representative of the first angular rate ofrotation of the vehicle and the second parameter representative of thesecond angular rate of rotation of the vehicle.
 27. The apparatusaccording to claim 18, wherein the processor is configured to estimatethe angular position of the vehicle by determining the inverse tangentof the ratio of said first angular rate of rotation and said secondangular rate of rotation.
 28. The apparatus according to claim 19,wherein the processor is configured to estimate the pitch of the vehiclein accordance with:$\theta = {\tan^{- 1}\left( \frac{- G_{X}}{G_{Z}} \right)}$ where G_(X)is the first angular rate of rotation, G_(Z) is the second angular rateof rotation, and Θ is the estimated pitch of the vehicle.
 29. Theapparatus according to claim 19, wherein the processor is configured toestimate a change in altitude of the vehicle using the estimated pitchof the vehicle.
 30. The apparatus according to claim 19, wherein theprocessor is configured to estimate a position of the vehicle in threedimensions using the estimated pitch of the vehicle.
 31. The apparatusaccording to claim 18, wherein the processor is configured to calibratean alignment of the first and second angular rate sensors with thevehicle.
 32. The apparatus according to claim 31, wherein the processoris configured to calibrate the alignment periodically when GNSS signalsare available.
 33. (canceled)
 34. The apparatus according to claim 19,wherein the processor is configured to resolve a rate of change ofheading of the vehicle using the estimated pitch of the vehicle andwherein the processor is configured to resolve the rate of change ofheading using the estimated pitch of the vehicle only when a yaw rate ofthe vehicle exceeds a threshold yaw rate value.
 35. A method ofdetermining an angular position of a vehicle, comprising: detecting afirst angular rate of rotation of the vehicle about a first axis ofrotation using a first angular rate sensor mounted to the vehicle;detecting a second angular rate of rotation of the vehicle about asecond axis of rotation using a second angular rate sensor mounted tothe vehicle, the second axis of rotation being substantially orthogonalto the first axis of rotation; estimating the angular position of thevehicle using the first angular rate of rotation of the vehicle and thesecond angular rate of rotation of the vehicle; and estimating a changein location of the vehicle using the estimated angular position of thevehicle.
 36. An apparatus configured to be mountable to a vehicle fordetermining an angular position of the vehicle, comprising: a firstangular rate sensor configured to detect a first angular rate ofrotation of the vehicle about a first axis of rotation; a second angularrate sensor configured to detect a second angular rate of rotation ofthe vehicle about a second axis of rotation, the second axis of rotationbeing substantially orthogonal to the first axis of rotation; and aprocessor configured to estimate the angular position of the vehicleusing the first angular rate of rotation of the vehicle and the secondangular rate of rotation of the vehicle and the processor configured toestimate a change in location of the vehicle using the estimated angularposition of the vehicle.
 37. The method according to claim 35, whereinthe vehicle experiences a rate of change of rotation about the firstaxis that is negligible while said detecting the first angular rate ofrotation of the vehicle and said detecting the second angular rate ofrotation of the vehicle are performed.
 38. The method according to claim35, wherein the angular position comprises a pitch of the vehicle andthe method further comprises resolving a rate of change of heading ofthe vehicle using the estimated pitch of the vehicle.
 39. The methodaccording to claim 35, wherein said estimating the angular position ofthe vehicle comprises determining the inverse tangent of a ratio of saidfirst angular rate of rotation and said second angular rate of rotation.40. The apparatus according to claim 36, wherein the apparatus isconfigured to detect the first angular rate of rotation of the vehicleand the second angular rate of rotation of the vehicle simultaneouslywhile the vehicle experiences a rate of change of rotation about thefirst axis that is negligible.
 41. The apparatus according to claim 36,wherein the angular position comprises a pitch of the vehicle and themethod further comprises resolving a rate of change of heading of thevehicle using the estimated pitch of the vehicle.
 42. The methodaccording to claim 36, wherein said estimating the angular position ofthe vehicle comprises determining the inverse tangent of a ratio of saidfirst angular rate of rotation and said second angular rate of rotation.